<PAGE>   1
                                                                    EXHIBIT 4.13


                               SECURITY AGREEMENT


          THIS SECURITY AGREEMENT (as amended, supplemented, amended and
restated or otherwise modified from time to time, this "Agreement"), dated as of
July 23, 1999 (the "Closing Date"), is made by STERLING CHEMICALS, INC., a
Delaware corporation, STERLING CANADA, INC., a Delaware corporation, STERLING
PULP CHEMICALS, INC., a Georgia corporation, STERLING PULP CHEMICALS US, INC., a
Delaware corporation, STERLING FIBERS, INC., a Delaware corporation, STERLING
CHEMICALS ENERGY, INC., a Delaware corporation, and STERLING CHEMICALS
INTERNATIONAL, INC., a Delaware corporation (individually referred to as an
"Assignor", and collectively referred to as the "Assignors"), and HARRIS TRUST
COMPANY OF NEW YORK, a New York corporation, as indenture trustee and collateral
agent (the "Collateral Agent") for the benefit of the holders (the "Holders") of
the 12 3/8% Senior Secured Notes due 2006 of Sterling Chemicals, Inc.

                                   WITNESSETH:

          WHEREAS, the Assignors and the Collateral Agent, as trustee, have
entered into that certain indenture dated as of July 23, 1999 (as amended,
amended and restated, supplemented or otherwise modified from time to time, the
"Indenture"), pursuant to which Sterling Chemicals, Inc. issued $295 million in
the aggregate principal amount of 12 3/8% Senior Secured Notes due 2006
(together with any notes issued in replacement thereof or in exchange or
substitution therefor, the "Senior Secured Notes"); and

          WHEREAS, pursuant to the terms of that certain Revolving Credit
Agreement, dated as of July 23, 1999, by and among Sterling Chemicals, Inc.,
Sterling Canada, Inc., Sterling Pulp Chemicals US, Inc., Sterling Pulp
Chemicals, Inc., Sterling Fibers, Inc., Sterling Chemicals Energy, Inc. and
Sterling Chemicals International, Inc., as Borrowers (collectively,
"Borrowers"), various financial institutions, as lenders ("Lenders"), DLJ
Capital Funding, Inc., as syndication agent ("Syndication Agent"), The CIT
Group/Business Credit, Inc., as the administrative agent (the "Administrative
Agent"), and Credit Suisse First Boston, as the documentation agent (as amended,
supplemented, amended and restated or otherwise modified from time to time, the
"Credit Agreement"), the Lenders have agreed to make Fixed Assets Loans (as
defined in the Credit Agreement) (collectively, the "Senior Loan") to the
Borrowers in the maximum original principal amount of Seventy Million Dollars
($70,000,000), the payment of which is secured (pursuant to the terms of the
Fixed Assets Security Agreement, dated as of July 23, 1999 (the "Fixed Assets
Security Agreement")) by, inter alia, a first priority security interest in the
Collateral (the "Senior Pledge") in favor of the Fixed Assets Secured Parties
and certain other parties to the Credit Agreement, as set forth on the signature
pages thereto or as may be added from time to time pursuant to the terms
thereof.

          NOW, THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, and in order to induce the Holders
to enter into the Indenture, each Assignor jointly and severally agrees, for the
benefit of each Holder, as follows:


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                                   ARTICLE I
                                  DEFINITIONS

          SECTION 1.1. Certain Terms. The following terms (whether or not
underscored) when used in this Agreement, including its preamble and recitals,
shall have the following meanings (such definitions to be equally applicable to
the singular and plural forms thereof):

          "Agreement" is defined in the preamble.

          "Closing Date" is defined in the preamble.

          "Collateral" is defined in Section 2.1.

          "Collateral Agent" is defined in the preamble.

          "Current Assets Security Agreement" is defined in the Credit
Agreement.

          "Equipment" has the meaning as defined in Section 9-109 of the U.C.C.

          "Fixed Assets Security Agreement" is defined in the recitals.

          "Holders" is defined in the preamble.

          "Indenture" is defined in the recitals.

          "Material Contracts" means all service contracts, supply contracts and
contract rights, but only to the extent necessary or appropriate for the
continued operation of the plants located at the Real Properties, as the
business thereupon is now conducted.

          "Obligations" is defined in Section 2.5.

          "Patent Collateral" means:

               (a) all letters patent and applications for letters patent in the
          United States, including all patent applications in preparation for
          filing in the United States and including each patent and patent
          application referred to in Item A of Schedule II attached hereto;

               (b) all reissues, divisions, continuations,
          continuations-in-part, extensions, renewals and reexaminations of any
          of the items described in clause (a);

               (c) all patent licenses in the United States, including each
          patent license referred to in Item B of Schedule II attached hereto;
          and

               (d) all proceeds of, and rights associated with, the foregoing
          (including license royalties and proceeds of infringement suits), the
          right to sue third parties for past, present or future infringements
          of any patent or patent application, referred to in clauses (a) or (b)
          above, and for breach or enforcement of any patent license referred to
          in clause (c) above;


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but only to the extent any of the foregoing is necessary or appropriate for the
continued operation of the plants located at the Real Properties, as the
business thereupon is now conducted.

          "Real Properties" means the plant facilities of the Assignors located
in Lowndes County, Georgia, Galveston County, Texas and Santa Rosa County,
Florida.

          "Satisfaction Date" means the date on which all Obligations have been
paid in full or otherwise satisfied

          "Senior Loan" is defined in the preamble.

          "Senior Secured Notes" is defined in the preambles.

          SECTION 1.2. Indenture Definitions. Unless otherwise defined herein or
the context otherwise requires, terms used in this Agreement, including its
preamble and recitals, have the meanings provided in the Indenture.

          SECTION 1.3. U.C.C. Definitions. Unless otherwise defined herein or in
the Indenture or the context otherwise requires, terms for which meanings are
provided in the Uniform Commercial Code from time to time in effect in the State
of New York (the "U.C.C.") are used in this Agreement, including its preamble
and recitals, with such meanings.


                                   ARTICLE II
                                SECURITY INTEREST

          SECTION 2.1. Grant of Security. Each Assignor hereby assigns, pledges,
hypothecates, charges, delivers, and transfers to the Collateral Agent for its
benefit and the ratable benefit of the Holders and hereby grants to the
Collateral Agent for its benefit and the ratable benefit of the Holders a
security interest in all of the following (collectively, the "Collateral"):

               (a) the real property, buildings, structures and other
          improvements to any of the foregoing, of the Assignors and to the
          extent any of the following items of property constitute fixtures
          and/or equipment under applicable laws, all fixtures, fittings,
          appliances, apparatus, Equipment, machinery, building and construction
          materials and other articles of every kind and nature whatsoever and
          all replacements thereof, now or hereafter affixed or attached to,
          placed upon or used in any way in connection with the complete and
          comfortable use, enjoyment, occupation, operation, development and/or
          maintenance of the Real Property of the Assignors or such buildings,
          structures and other improvements, the Patent Collateral and the
          Material Contracts;

               (b) all products, offspring, rents, issues, profits, returns,
          income and proceeds of and from any and all of the foregoing
          Collateral (including proceeds which constitute property of the types
          described in clause (a) and, to the extent not otherwise included, all
          payments under insurance (whether or not the Collateral Agent is the
          loss payee thereof) or any indemnity, warranty or guaranty, payable by
          reason of loss or damage to or otherwise with respect to any of the
          foregoing Collateral).


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Notwithstanding the foregoing, "Collateral" shall not include (a) any general
intangibles or other rights arising under any contracts, instruments, licenses
or other documents as to which the grant of a security interest would constitute
a violation of a valid and enforceable restriction in favor of a third party on
such grant, unless and until any required consents shall have been obtained or
(b) any Collateral (as defined in the Current Assets Security Agreement). Each
Assignor agrees to use its best efforts to obtain any such required consent with
respect to any material item of Collateral.

          SECTION 2.2. Security for Obligations. This Agreement secures the
payment in cash in full of all Obligations under the Indenture and the Senior
Secured Notes.

          SECTION 2.3. Continuing Security Interest. This Agreement shall create
a continuing security interest in the Collateral and shall:

               (a) remain in full force and effect until the satisfaction of all
          obligations under the Indenture and Senior Secured Notes (the
          "Obligations");

               (b) be binding upon each Assignor, its successors, transferees
          and assigns; and

               (c) inure, together with the rights and remedies of the
          Collateral Agent hereunder, to the benefit of the Collateral Agent and
          the Holders.

          SECTION 2.4. Assignor Remains Liable. Anything herein to the contrary
notwithstanding:

               (a) each Assignor will remain liable under the contracts and
          agreements included in the Collateral to the extent set forth therein,
          and will perform all of its duties and obligations under such
          contracts and agreements to the same extent as if this Agreement had
          not been executed;

               (b) the exercise by the Collateral Agent of any of its rights
          hereunder will not release any Assignor from any of its duties or
          obligations under any such contracts or agreements included in the
          Collateral; and

               (c) neither the Collateral Agent nor any Holder will have any
          obligation or liability under any such contracts or agreements
          included in the Collateral by reason of this Agreement, nor will the
          Collateral Agent or any other Collateral Agent or any Holder be
          obligated to perform any of the obligations or duties of any Assignor
          thereunder or to take any action to collect or enforce any claim for
          payment assigned hereunder.

          SECTION 2.5. Security Interest Absolute. All rights of the Collateral
Agent and the security interests granted to the Collateral Agent hereunder, and
all obligations of each Assignor hereunder, shall be absolute and unconditional,
irrespective of:

               (a) any lack of validity or enforceability of the Indenture or
          any Security Agreement;

               (b) the failure of the Collateral Agent or any Holder


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                   (i) to assert any claim or demand or to enforce any right or
               remedy against the Assignors or any other Person under the
               provisions of the Indenture or any Security Agreement or
               otherwise or

                   (ii) to exercise any right or remedy against any guarantor
               of, or collateral securing, any Obligations;

               (c) any change in the time, manner or place of payment of, or in
          any other term of, all or any of the Obligations or any other
          extension, compromise or renewal of any Obligations;

               (d) any reduction, limitation, impairment or termination of any
          Obligations for any reason (other than the repayment in full and in
          cash of all Obligations), including any claim of waiver, release,
          surrender, alteration or compromise, and shall not be subject to (and
          each Assignor hereby waives any right to or claim of) any defense or
          set-off, counterclaim, recoupment or termination whatsoever by reason
          of the invalidity, illegality, nongenuineness, irregularity,
          compromise or unenforceability of, or any other event or occurrence
          affecting, any Obligations or otherwise;

               (e) any amendment to, rescission, waiver or other modification
          of, or any consent to departure from, any of the terms of the
          Indenture or any Security Agreement;

               (f) any addition, exchange, release, surrender or non-perfection
          of any collateral (including the Collateral), or any amendment to or
          waiver or release of or addition to or consent to departure from any
          guaranty, for any of the Obligations; or

               (g) any other circumstances which might otherwise constitute a
          defense available to, or a legal or equitable discharge of, any
          Assignor, any surety or any guarantor.

          SECTION 2.6. Postponement of Subrogation, etc. Each Assignor hereby
agrees that it will not exercise any rights which it may acquire by reason of
any payment made hereunder, whether by way of subrogation, reimbursement or
otherwise, until the Satisfaction Date. Any amount paid to any Assignor on
account of any payment made hereunder prior to the Satisfaction Date shall be
held in trust for the benefit of the Collateral Agent and the Holders of the
Senior Secured Notes and shall immediately be paid to the Collateral Agent for
the ratable benefit of the Holders of the Senior Secured Notes and credited and
applied against the Obligations, whether matured or unmatured, in accordance
with the terms of the Indenture; provided, however, that if:

               (a) such Assignor has made payment to the Collateral Agent for
          the ratable benefit of the Holders of the Senior Secured Notes of all
          or any part of the Obligations; and

               (b) the Satisfaction Date has occurred,

the Collateral Agent, on behalf of the Holders of the Senior Secured Notes,
agrees that, at the requesting Assignor's request, the Collateral Agent, on
behalf of the Collateral Agent and the Holders of the Senior Secured Notes, will
execute and deliver to such Assignor appropriate


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<PAGE>   6

documents (without recourse and without representation or warranty) necessary to
evidence the transfer by subrogation to such Assignor of an interest in the
Obligations resulting from such payment by such Assignor. In furtherance of the
foregoing, prior to the Satisfaction Date, each Assignor shall refrain from
taking any action or commencing any proceeding against any Assignor (or its
successors or assigns, whether in connection with a bankruptcy proceeding or
otherwise) to recover any amounts in respect of payments made under this
Agreement to the Collateral Agent or Holders of the Senior Secured Notes.


                   ARTICLE III REPRESENTATIONS AND WARRANTIES

          SECTION 3.1. Representations and Warranties. Each Assignor represents
and warrants to the Collateral Agent and the Holders as set forth in this
Article III.

          SECTION 3.2. Ownership, No Liens, etc. Each Assignor owns its
Collateral free and clear of any Lien, except for the security interest created
by this Agreement, the Lien in favor of the Fixed Assets Secured Parties (as
such term is defined in the Credit Agreement) and the Permitted Liens. No
effective financing statement or other instrument similar in effect covering all
or any part of the Collateral is on file in any recording office, except such as
may have been filed in favor of the Collateral Agent relating to this Agreement
or as have been filed in connection with the Fixed Assets Security Agreement and
Permitted Liens.

          SECTION 3.3. Validity, etc. This Agreement creates a valid second
priority security interest in the Collateral securing the payment of the
Obligations, and the Assignors will at all times cause the security interests
granted pursuant to this Agreement to constitute valid perfected second priority
security interests (and, upon the expiration or termination of the Senior Debt
Intercreditor Agreement, first priority security interests) in the Collateral,
enforceable as such against all creditors of Assignor and (except as otherwise
specifically provided herein) any Persons purporting to purchase any Collateral
from Assignor. Assignor will, promptly upon request by Collateral Agent, execute
and deliver or cause to be executed and delivered, or use its best efforts to
procure, tax stamps, assignments, instruments and other documents, all in form
and substance reasonably satisfactory to the Collateral Agent, and take any
other actions that are necessary or, in the reasonable opinion of Collateral
Agent, desirable to perfect, continue the perfection of, or protect the second
(or, upon the expiration or termination of the Senior Debt Intercreditor
Agreement, first) priority of the Collateral Agent's security interest in the
Collateral, to protect the Collateral against the rights, claims or interests of
third persons (subject to the terms of the Senior Debt Intercreditor Agreement),
to enable the Collateral Agent to exercise or enforce its rights and remedies
hereunder, or otherwise to effect the purposes of this Agreement. Assignor also
hereby authorizes the Collateral Agent to file any financing or continuation
statements with respect to the Collateral without the signature of Assignor to
the extent permitted by applicable law. Assignor will pay all costs incurred in
connection with any of the foregoing.

          SECTION 3.4. Authorization, Approval, etc. Except as have been
obtained or made and are in full force and effect, no material authorization,
material approval or other action by, and no material notice to or material
filing with, any Governmental Authority or regulatory body is required either
(a) for the grant by such Assignor of the security interest granted hereby, the


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pledge by such Assignor of any Collateral pursuant hereto or for the execution,
delivery and performance of this Agreement by such Assignor or (b) for the
perfection of or the exercise by the Collateral Agent of its rights and remedies
hereunder.

          SECTION 3.5. Compliance with Laws. Such Assignor is in compliance with
the requirements of all applicable laws (including the provisions of the Fair
Labor Standards Act), rules, regulations and orders of every Governmental
Authority, the non-compliance with which could reasonably be expected to have a
Material Adverse Effect or which could reasonably be expected to materially
adversely affect the value of the Collateral.


                              ARTICLE IV COVENANTS

          SECTION 4.1. Further Assurances, etc. Such Assignor agrees that, from
time to time at its own expense, it will promptly execute and deliver all
further instruments and documents, and take all further action, that may be
necessary or desirable, or that the Collateral Agent may reasonably request, in
order to perfect, preserve and protect any security interest granted or
purported to be granted hereby or to enable the Collateral Agent to exercise and
enforce its rights and remedies hereunder with respect to any Collateral.
Without limiting the generality of the foregoing and subject to the terms of the
Senior Debt Intercreditor Agreement, such Assignor will:

               (a) execute and file such financing or continuation statements,
          or amendments thereto, and such other instruments or notices as may be
          necessary or desirable, or as the Collateral Agent may request, in
          order to perfect and preserve the security interests and other rights
          granted or purported to be granted to the Collateral Agent hereby; and

               (b) furnish to the Collateral Agent, from time to time at the
          Collateral Agent's request, statements and schedules further
          identifying and describing the Collateral and such other reports in
          connection with the Collateral as the Collateral Agent may reasonably
          request, all in reasonable detail.

With respect to the foregoing and the grant of the security interest hereunder,
such Assignor hereby authorizes the Collateral Agent to file one or more
financing or continuation statements, and amendments thereto, relative to all or
any part of the Collateral without the signature of such Assignor where
permitted by law. A carbon, photographic or other reproduction of this Agreement
or any financing statement covering the Collateral or any part thereof shall be
sufficient as a financing statement where permitted by law.


                         ARTICLE V THE COLLATERAL AGENT

          SECTION 5.1. Collateral Agent Appointed Attorney-in-Fact. Each
Assignor hereby irrevocably appoints the Collateral Agent as such Assignor's
attorney-in-fact, with full authority and in the name, place and stead of the
Assignor or in its own name, from time to time in the Collateral Agent's
discretion, to take, upon the occurrence and during the continuance of an Event
of Default, any action and to execute any instrument which the Collateral Agent
may deem


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necessary or advisable to accomplish the purposes of this Agreement, including
without limitation:

               (a) to ask, demand, collect, sue for, recover, compromise and
          receive and give acquittance and receipts for moneys due and to become
          due under or in respect of any of the Collateral;

               (b) to receive, endorse and collect any drafts or other
          instruments, documents and chattel paper, in connection with clause
          (a) above;

               (c) to file any claims or take any action or institute any
          proceedings which the Collateral Agent may deem necessary or desirable
          for the collection of any of the Collateral or otherwise to enforce
          the rights of the Collateral Agent with respect to any of the
          Collateral; and

               (d) to perform the affirmative obligations of such Assignor
          hereunder (including all obligations of such Assignor pursuant to
          Section 4.1).

          SECTION 5.2. Authority of Collateral Agent. The Collateral Agent shall
have and be entitled to exercise all powers hereunder that are specifically
granted to Collateral Agent by the terms hereof, together with such powers as
are reasonably incidental thereto. The Collateral Agent may perform any of its
duties hereunder or in connection with the Collateral by or through agents or
employees and shall be entitled to retain counsel and to act in reliance upon
the advice of counsel concerning all such matters. Neither the Collateral Agent
nor any director, officer, employee, attorney or agent of the Collateral Agent
shall be responsible for the validity, effectiveness or sufficiency hereof or of
any document or security furnished pursuant hereto. The Collateral Agent and its
directors, officers, employees, attorneys and agents shall be entitled to rely
on any communication, instrument or document reasonably believed by it or them
to be genuine and correct and to have been signed or sent by the proper person
or persons.

          Each Assignor acknowledges that the rights and responsibilities of the
Collateral Agent under this Agreement with respect to any action taken by the
Collateral Agent or the exercise or non-exercise by the Collateral Agent of any
option, right, request, judgment or other right or remedy provided for herein or
resulting or arising out of this Agreement shall, as between the Collateral
Agent and the Holders of the Senior Secured Notes, be governed by the Indenture
and by such other agreements with respect thereto as may exist from time to time
among them, but, as between the Collateral Agent and Assignor, the Collateral
Agent shall be conclusively presumed to be acting as agent for the Holders of
the Senior Secured Notes with full and valid authority so to act or refrain from
acting, and Assignor shall not be obligated or entitled to make any inquiry
respecting such authority.

          SECTION 5.3. Resignation or Removal of the Collateral Agent. Until
such time as the Obligations shall have been paid in full, the Collateral Agent
may at any time, by giving written notice to the Assignors, the Trustee (as
defined in the Indenture) and the Holders of the Senior Secured Notes, resign
and be discharged of the responsibilities hereby created, such resignation to
become effective upon (i) the appointment of a successor Collateral Agent and
(ii) the acceptance of such appointment by such successor Collateral Agent. As
promptly as


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practicable after the giving of any such notice, the Trustee (if the Trustee is
not then acting as the Collateral Agent hereunder) or if the Trustee and the
Collateral Agent are the same person or entity, the Holders of the Senior
Secured Notes shall appoint a successor Collateral Agent, which successor
Collateral Agent shall be reasonably acceptable to Assignor. If no successor
Collateral Agent shall be appointed and shall have accepted such appointment
within 90 days after the Collateral Agent gives the aforesaid notice of
resignation, the Collateral Agent may apply to any court of competent
jurisdiction to appoint a successor Collateral Agent to act until such time, if
any, as a successor shall have been appointed as provided in this Section 5.3.
Any successor so appointed by such court shall immediately and without further
act be superseded by any successor Collateral Agent appointed by the Holders of
the Senior Secured Notes, as provided in this Section 5.3. Any Collateral Agent
that has resigned shall be entitled to fees, costs and expenses to the extent
incurred or arising, or relating to events occurring, before its resignation or
removal.

          SECTION 5.4. Release; Termination of Agreement. This Agreement shall
terminate upon the earlier to occur of (i) the Satisfaction Date, (ii) the day
of the Legal Defeasance of all of the Obligations pursuant to Section 8.02 of
the Indenture (other than those surviving Obligations specified therein) and
(iii) such other termination date as is provided in the Indenture. At such time,
the Collateral Agent shall, at the request of Assignor, reassign and redeliver
to Assignor all of the Collateral hereunder that has not been sold, disposed of,
retained or applied by the Collateral Agent in accordance with the terms hereof.
Such reassignment and redelivery shall be without warranty by or recourse to the
Collateral Agent, except as to the absence of any prior assignments by the
Collateral Agent of its interest in the Collateral, and shall be at the expense
of Assignor.

          Assignor agrees that it will not, except as permitted by the
Indenture, sell or dispose of, or grant any option or warrant with respect to,
any of the Collateral; provided, however, that if Assignor shall sell any of the
Collateral in accordance with the terms of the Indenture, the Collateral Agent
shall, at the request of Assignor and subject to requirements of Section 10.03
of the Indenture, release the Collateral subject to such sale free and clear of
the Lien under this Agreement.

          SECTION 5.5. Collateral Agent Has No Duty. The powers conferred on the
Collateral Agent hereunder are solely to protect its interest (on behalf of the
Collateral Agent and the Holders of the Senior Secured Notes) in the Collateral
and shall not impose any duty on it to exercise any such powers. Except for
reasonable care of any Collateral in its possession and the accounting for
moneys actually received by it hereunder, the Collateral Agent shall have no
duty as to any Collateral or responsibility for:

               (a) ascertaining or taking action with respect to calls,
          conversions, exchanges, maturities, tenders or other matters relative
          to any investment property, whether or not the Collateral Agent has or
          is deemed to have knowledge of such matters; or

               (b) taking any necessary steps to preserve rights against prior
          parties or any other rights pertaining to any Collateral.


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<PAGE>   10

          SECTION 5.6. Reasonable Care. The Collateral Agent is required to
exercise reasonable care in the custody and preservation of any of the
Collateral in its possession; provided, however, that the Collateral Agent shall
be deemed to have exercised reasonable care in the custody and preservation of
any of the Collateral, if it takes such action for that purpose as any Assignor
reasonably requests in writing from time to time, but failure of the Collateral
Agent to comply with any such request at any time shall not in itself be deemed
a failure to exercise reasonable care. If an Event of Default has occurred and
is continuing, the Collateral Agent shall not be required to comply with any
request of the Assignor with respect to the matters described in this Section.


                              ARTICLE VI REMEDIES

          SECTION 6.1. Certain Remedies. If any Event of Default shall have
occurred and be continuing:

               (a) The Collateral Agent may exercise in respect of the
          Collateral, in addition to other rights and remedies provided for
          herein or otherwise available to it, all the rights and remedies of a
          secured party on default under the U.C.C. (whether or not the U.C.C.
          applies to the affected Collateral) and also may

                   (i) require each Assignor to, and such Assignor hereby agrees
               that it will, at its expense and upon request of the Collateral
               Agent forthwith, assemble all or part of the Collateral as
               directed by the Collateral Agent and make it available to the
               Collateral Agent at a place to be designated by the Collateral
               Agent which is reasonably convenient to both parties, and

                   (ii) without notice except as specified below, sell the
               Collateral or any part thereof in one or more parcels at public
               or private sale, at any of the Collateral Agent's offices or
               elsewhere, for cash, on credit or for future delivery, and upon
               such other terms as the Collateral Agent may deem commercially
               reasonable. Each Assignor agrees that, to the extent notice of
               sale shall be required by law, at least ten days prior notice to
               such Assignor of the time and place of any public sale or the
               time after which any private sale is to be made shall constitute
               reasonable notification. The Collateral Agent shall not be
               obligated to make any sale of such Collateral regardless of
               notice of sale having been given. The Collateral Agent may
               adjourn any public or private sale from time to time by
               announcement at the time and place fixed therefor, and such sale
               may, without further notice, be made at the time and place to
               which it was so adjourned.

               (b) All cash proceeds received by the Collateral Agent in respect
          of any sale of, collection from or other realization upon all or any
          part of the Collateral shall be applied by the Collateral Agent
          against all or any part of the Obligations as follows:

                   (i) first, to the payment of any amounts payable to the
               Collateral Agent pursuant to the Indenture and Section 6.3;


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                   (ii) second, to the equal and ratable payment of any
               Obligations owed to Collateral Agent or any Holder of the Senior
               Secured Notes pursuant to the Indenture or any other Security
               Agreement, applied

                        (A) first to fees and expense reimbursements then due to
                    such Collateral;

                        (B) then to interest due to such Collateral Agent;

                        (C) then to pay the remaining outstanding Obligations;

                   (iii) third, to be held as additional collateral security
               until the Satisfaction Date, after which such remaining cash
               proceeds shall be paid over to the applicable Assignor or to
               whomsoever may be lawfully entitled to receive such surplus.

               (c) The Collateral Agent may

                   (i) transfer all or any part of the Collateral into the name
               of the Collateral Agent or its nominee, with or without
               disclosing that such Collateral is subject to the lien and
               security interest hereunder,

                   (ii) enforce collection of any of the Collateral by suit or
               otherwise, and surrender, release or exchange all or any part
               thereof, or compromise or extend or renew for any period (whether
               or not longer than the original period) any obligations of any
               nature of any party with respect thereto,

                   (iii) take control of any proceeds of the Collateral and

                   (iv) execute (in the name, place and stead of such Assignor),
               assignments and other instruments of conveyance or transfer with
               respect to all or any of the Collateral.

          SECTION 6.2. Compliance with Restrictions. Each Assignor agrees that
in any sale of any of the Collateral whenever an Event of Default shall have
occurred and be continuing, the Collateral Agent is hereby authorized to comply
with any limitation or restriction in connection with such sale as it may be
advised by counsel is necessary in order to avoid any violation of applicable
law or in order to obtain any required approval of the sale or of the purchaser
by any Governmental Authority or official, and such Assignor further agrees that
such compliance shall not result in such sale being considered or deemed not to
have been made in a commercially reasonable manner, nor shall the Collateral
Agent be liable nor accountable to such Assignor for any discount allowed by the
reason of the fact that such Collateral is sold in compliance with any such
limitation or restriction.

          SECTION 6.3. Indemnity and Expenses. Each Assignor hereby jointly and
severally indemnifies and holds harmless the Collateral Agent from and against
any and all claims, losses and liabilities arising out of or resulting from this
Agreement (including enforcement of this Agreement), except claims, losses or
liabilities resulting from the Collateral Agent's gross


                                      -11-
<PAGE>   12

negligence or willful misconduct and each Assignor will, upon demand pay to the
Collateral Agent the amount of any and all reasonable expenses, including the
reasonable fees and disbursements of its counsel and of any experts and agents,
which the Collateral Agent may incur, in each case, in connection with:

               (a) the administration of this Agreement;

               (b) the custody, preservation, use, or operation of or the sale
          of, collection from, or other realization upon, any of the Collateral;

               (c) the exercise or enforcement of any of the rights of the
          Collateral Agent hereunder; or

               (d) the failure by any Assignor to perform or observe any of the
          provisions hereof.


                      ARTICLE VII MISCELLANEOUS PROVISIONS

          SECTION 7.1. Security Agreement. This Agreement is a Security
Agreement executed pursuant to the Indenture and shall (unless otherwise
expressly indicated herein) be construed, administered and applied in accordance
with the terms and provisions thereof.

          SECTION 7.2. Amendments; etc. No amendment to or waiver of any
provision of this Agreement nor consent to any departure by any Assignor
herefrom shall in any event be effective unless the same shall be in writing and
signed by the Collateral Agent (on behalf of the Holders of the Senior Secured
Notes) and each Assignor and then such waiver or consent shall be effective only
in the specific instance and for the specific purpose for which given.

          SECTION 7.3. Protection of Collateral. The Collateral Agent may from
time to time, at its option, perform any act which each Assignor agrees
hereunder to perform and which such Assignor shall fail to perform after being
requested in writing so to perform (it being understood that no such request
need be given after the occurrence and during the continuance of an Event of
Default) and the Collateral Agent may from time to time take any other action
which the Collateral Agent reasonably deems necessary for the maintenance,
preservation or protection of any of the Collateral or of its security interest
therein.

          SECTION 7.4. Addresses for Notices. All notices and other
communications provided for hereunder shall be in writing and addressed,
delivered or transmitted, if to any Assignor, at the address or facsimile number
of the Company provided for in the Indenture, and if to the Collateral Agent, at
the following address or facsimile number: Harris Trust Company of New York,
Wall Street Plaza, 19th Floor, 88 Pine Street, New York, NY 10005, Facsimile
No.: (212) 701-7664, Attn: Peter Morse, or as to any such party, at such other
address or facsimile number as shall be designated by such party in a written
notice to each other party complying as to delivery with the terms of this
Section. Any notice, (a) if mailed and properly addressed with postage prepaid
or if properly addressed and sent by pre-paid courier service, shall be deemed
given when received, or (b) if transmitted by facsimile, shall be deemed given
when transmitted (and telephonic confirmation of receipt thereof has been
received).


                                      -12-
<PAGE>   13

          SECTION 7.5. Headings. The various headings of this Agreement are
inserted for convenience only, and shall not affect the meaning or
interpretation of this Agreement or any provisions thereof.

          SECTION 7.6. Severability. Any provision of this Agreement which is
prohibited or unenforceable in any jurisdiction shall, as to such provision and
such jurisdiction, be ineffective to the extent of such prohibition or
unenforceability without invalidating the remaining provisions of this Agreement
or affecting the validity or enforceability of such provision in any other
jurisdiction.

          SECTION 7.7. Counterparts; Effectiveness. This Agreement may be
executed by the parties hereto in several counterparts, each of which shall be
deemed to be an original (whether such counterpart is originally executed or an
electronic copy of an original) and all of which shall constitute together but
one and the same agreement. This Agreement shall become effective as of the date
first above written and be binding upon a Assignor when a counterpart hereof
executed on behalf of such Assignor shall have been received by the Collateral
Agent.

          SECTION 7.8. Governing Law. THIS AGREEMENT SHALL BE DEEMED TO BE A
CONTRACT MADE UNDER AND GOVERNED BY THE INTERNAL LAWS OF THE STATE OF NEW YORK,
EXCLUDING THE LAW OF CONFLICTS EXCEPT TO THE EXTENT THAT THE VALIDITY OR
PERFECTION OF THE SECURITY INTEREST HEREUNDER, OR REMEDIES HEREUNDER, IN RESPECT
OF ANY PARTICULAR COLLATERAL ARE GOVERNED BY THE LAWS OF A JURISDICTION OTHER
THAN THE STATE OF NEW YORK.

          SECTION 7.9. Agreement Subject to the Senior Debt Intercreditor
Agreement. Notwithstanding anything to the contrary contained herein, it is
expressly understood and agreed by the parties hereto that this Agreement shall
be subject to the terms of the Senior Debt Intercreditor Agreement.

                [REMAINDER OF THIS PAGE INTENTIONALLY LEFT BLANK]


                                      -13-
<PAGE>   14

          IN WITNESS WHEREOF, each Assignor has caused this Agreement to be duly
executed and delivered by its officer thereunto duly authorized as of the date
first above written.

                                          STERLING CHEMICALS, INC.


                                          By
                                            ------------------------------------
                                            Title:


                                          STERLING CANADA, INC.


                                          By
                                            ------------------------------------
                                            Title:


                                          STERLING PULP CHEMICALS US, INC.


                                          By
                                            ------------------------------------
                                            Title:


                                          STERLING PULP CHEMICALS, INC.


                                          By
                                            ------------------------------------
                                            Title:


                                          STERLING FIBERS, INC.


                                          By
                                            ------------------------------------
                                            Title:


                                          STERLING CHEMICALS ENERGY, INC.


                                          By
                                            ------------------------------------
                                            Title:


                                          STERLING CHEMICALS INTERNATIONAL, INC.


                                          By
                                            ------------------------------------
                                            Title:


                                      -14-
<PAGE>   15

                                        HARRIS TRUST COMPANY OF NEW YORK.
                                           as Collateral Agent, on behalf of the
                                           Holders  of the Senior Secured Notes


                                        By
                                          --------------------------------------
                                          Title:


                                      -15-
<PAGE>   16

                                   SCHEDULE I
                              to Security Agreement


([NAME OF ASSIGNOR])


Item A. Patents


Issued Patents

        Patent No.           Issue Date          Inventor(s)         Title





Pending Patent Applications

        Serial No.           Filing Date         Inventor(s)         Title





Patent Applications in Preparation

                             Expected
        Docket No.           Filing Date         Inventor(s)         Title





Item B. Patent Licenses

                                       Effective       Expiration        Subject
        Licensor    Licensee              Date            Date           Matter





<PAGE>   17

EXHIBIT A TO SECURITY AGREEMENT


                            PATENT SECURITY AGREEMENT


          This PATENT SECURITY AGREEMENT (this "Agreement"), dated as of________
__, ____, is made between ___________________, a ____________________ (the
"Assignor"), and HARRIS TRUST COMPANY OF NEW YORK, as Collateral Agent (together
with any successor(s) thereto in such capacity, the "Collateral Agent") for each
of the Collateral Agent and the Holders of the Senior Secured Notes.


                                   WITNESSETH:

          WHEREAS, Sterling Chemicals, Inc., Sterling Canada, Inc., Sterling
Pulp Chemicals, Inc., Sterling Pulp Chemicals, US, Inc., Sterling Fibers, Inc.,
Sterling Chemicals Energy, Inc., and Sterling Chemicals International, Inc., and
the Collateral Agent, as trustee, have entered into that certain indenture dated
as of July 23, 1999 (as amended, amended and restated, supplemented or otherwise
modified from time to time, the "Indenture"), pursuant to which Sterling
Chemicals, Inc. issued $295 million in the aggregate principal amount of 123/8%
Senior Secured Notes due 2006 (together with any notes issued in replacement
thereof or in exchange or substitution therefor, the "Senior Secured Notes");
and

          WHEREAS, the terms of the Indenture require that the Assignor (i)
pledge to the Collateral Agent for the ratable benefit of the Holders (as
defined in the Indenture) of the Senior Secured Notes, and grant to the
Collateral Agent for the ratable benefit of the Holders of the Senior Secured
Notes a second priority security interest in the Collateral (as defined herein)
and (ii) execute and deliver this Agreement in order to secure the payment and
performance by the Assignor of all of its obligations under the Indenture and
the Senior Secured Notes (the "Obligations");

          NOW, THEREFORE, in consideration of the premises, the Assignor hereby
agrees with the Collateral Agent for its benefit and the ratable benefit of the
Holders of the Senior Secured Notes as follows:

          SECTION 1. Definitions. Unless otherwise defined herein or the context
otherwise requires, terms used in this Agreement, including its preamble and
recitals, have the meanings provided (or incorporated by reference) in the
Security Agreement dated July 23, 1999 by and among Sterling Chemicals, Inc.,
Sterling Canada, Inc., Sterling Pulp Chemicals, Inc., Sterling Pulp Chemicals,
US, Inc., Sterling Fibers, Inc., Sterling Chemicals Energy, Inc., Sterling
Chemicals International, Inc. and Harris Trust Company of New York as indenture
trustee and collateral agent for the benefit of the Holders of the Senior
Secured Notes.

          SECTION 2. Grant of Security Interest. For good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged, to
secure all of the Obligations, the Assignor does hereby pledge and hypothecate
to the Collateral Agent, and grant to the Collateral


                                   Exhibit A
                                      -1-
<PAGE>   18

Agent a security interest in, for its benefit and the benefit of each Holder,
all of the following property (the "Patent Collateral"), whether now owned or
hereafter acquired or existing by it:

               (e) all letters patent and applications for letters patent in the
          United States, including all patent applications in preparation for
          filing in the United States and including each patent and patent
          application referred to in Item A of Schedule I attached hereto;

               (f) all reissues, divisions, continuations,
          continuations-in-part, extensions, renewals and reexaminations of any
          of the items described in clause (a);

               (g) all patent licenses in the United States, including each
          patent license referred to in Item B of Schedule I attached hereto;
          and

               (h) all proceeds of, and rights associated with, the foregoing
          (including license royalties and proceeds of infringement suits), the
          right to sue third parties for past, present or future infringements
          of any patent or patent application, referred to in clauses (a) or (b)
          above, and for breach or enforcement of any patent license referred to
          in clause (c) above;

in each case, to the extent, but only to the extent, that any of the foregoing
is necessary or appropriate for the continued operation of the plant facilities
of Assignor located in Valdosta-Lowndes County, Georgia, Galveston County, Texas
and Santa Rosa County, Florida.

          SECTION 3. Security Agreement. This Agreement has been executed and
delivered by the Assignor for the purpose of registering the security interest
of the Collateral Agent in the Patent Collateral with the United States Patent
and Trademark Office. The security interest granted hereby has been granted as a
supplement to, and not in limitation of, the security interest granted to the
Collateral Agent for its benefit and the benefit of each Holder. The Security
Agreement (and all rights and remedies of the Collateral Agent and each Holder
thereunder) shall remain in full force and effect in accordance with its terms.

          SECTION 4. Release of Security Interest. Upon the earliest to occur of
(i) the sale, transfer or other disposition of any Patent Collateral in
accordance with the Indenture, (ii) the day of the Legal Defeasance of all
Obligations pursuant to Section 8.02 of the Indenture, (iii) the Satisfaction
Date and (iv) such other termination date as is provided in the Indenture, the
Collateral Agent shall, at the Assignor's expense, execute and deliver to the
Assignor all instruments and other documents as may be necessary or proper to
release the Lien on the Patent Collateral which has been granted hereunder.

          SECTION 5. Acknowledgment. The Assignor does hereby further
acknowledge and affirm that the rights and remedies of the Collateral Agent with
respect to the Lien on the Patent Collateral granted hereby are more fully set
forth in the Security Agreement, the terms and provisions of which (including
the remedies provided for therein) are incorporated by reference herein as if
fully set forth herein.


                                   Exhibit A
                                      -2-
<PAGE>   19

          SECTION 6. The Indenture or any other Security Agreements, etc. This
Agreement is a Security Agreement executed pursuant to the Indenture and shall
(unless otherwise expressly indicated herein) be construed, administered and
applied in accordance with the terms and provisions of the Indenture.

          SECTION 7. Counterparts. This Agreement may be executed by the parties
hereto in several counterparts, each of which shall be deemed to be an original
(whether such counterpart is originally executed or an electronic copy of an
original) and all of which shall constitute together but one and the same
agreement. This Agreement shall become effective and binding as of the date
first above written when a counterpart hereof executed on behalf of the Assignor
shall have been received by the Collateral Agent.

          SECTION 8. Agreement Subject to Senior Debt Intercreditor Agreement.
Notwithstanding anything to the contrary contained herein, it is expressly
understood and agreed by the parties hereto that this Agreement shall be subject
to the terms of the Senior Debt Intercreditor Agreement.

          IN WITNESS WHEREOF, the parties hereto have caused this Agreement to
be duly executed and delivered by their respective officers thereunto duly
authorized as of the day and year first above written.


                                         ASSIGNOR:


                                         By:
                                            ------------------------------------
                                            Title:
                                                  ------------------------------


                                         HARRIS TRUST COMPANY OF NEW YORK,
                                           as Collateral Agent, on behalf of the
                                            Holders of the Senior Secured Notes


                                         By:
                                            ------------------------------------
                                            Title:
                                                  ------------------------------


                                   Exhibit A
                                      -3-
<PAGE>   20

                                   SCHEDULE I
                          to Patent Security Agreement


Item A. Patents


                                 Issued Patents
                                 --------------

        Patent No.           Issue Date          Inventor(s)         Title
        ----------           ----------          -----------         -----




                          Pending Patent Applications
                          ---------------------------

        Serial No.           Filing Date         Inventor(s)         Title
        ----------           -----------         -----------         -----




                       Patent Applications in Preparation
                       ----------------------------------

                             Expected
        Docket No.           Filing Date         Inventor(s)         Title
        ----------           -----------         -----------         -----




Item B. Patent Licenses


                                       Effective       Expiration        Subject
        Licensor    Licensee              Date            Date           Matter
        --------    --------           ---------       ----------        -------