A method for producing a water-soluble thermally-crosslinkable polymeric material, comprising the steps of: obtaining a reactive mixture which is an aqueous solution comprising (a) an azetidinium-containing polymer having azetidinium groups, wherein the azetidinium-containing polymer is a poly(2-oxazoline-co-ethyleneimine)-epichlorohydrin or a homopolymer or copolymer of an azetidinium-containing vinylic monomer, (b) a hydrophilicity-enhancing agent which is non-ionic or positively charged at the pH of the aqueous solution, which pH is at least 9.0, and has at least one reactive functional group selected from the group consisting of primary amino group, secondary amino group, thiol group, and a combination thereof, and (c) one or more non-polymeric ionic compounds which are present in the aqueous solution in a total amount of 1 mM to 120 mM and are selected from the group consisting of sodium chloride, potassium chloride, salts of phosphoric acid, salts of boric acid, salts of citric acid, salts of carbonic acid, and combinations thereof; and heating the reactive mixture to reach a reaction temperature of from about 40°C to about 85°C and maintaining the temperature of the reactive mixture at the reaction temperature for a time period sufficient to obtain the water-soluble thermally-crosslinkable polymeric material in which the hydrophilicity-enhancing agent is covalently attached to the azetidinium-containing polymer through one or more covalent linkages each formed between one azetidinium group and one reactive functional group, wherein the water-soluble thermally-crosslinkable polymeric material comprises azetidinium groups. obtaining a reactive mixture which is an aqueous solution comprising (a) an azetidinium-containing polymer having azetidinium groups, wherein the azetidinium-containing polymer is a poly(2-oxazoline-co-ethyleneimine)-epichlorohydrin or a homopolymer or copolymer of an azetidinium-containing vinylic monomer, (b) a hydrophilicity-enhancing agent which is non-ionic or positively charged at the pH of the aqueous solution, which pH is at least 9.0, and has at least one reactive functional group selected from the group consisting of primary amino group, secondary amino group, thiol group, and a combination thereof, and (c) one or more non-polymeric ionic compounds which are present in the aqueous solution in a total amount of 1 mM to 120 mM and are selected from the group consisting of sodium chloride, potassium chloride, salts of phosphoric acid, salts of boric acid, salts of citric acid, salts of carbonic acid, and combinations thereof; and (a) an azetidinium-containing polymer having azetidinium groups, wherein the azetidinium-containing polymer is a poly(2-oxazoline-co-ethyleneimine)-epichlorohydrin or a homopolymer or copolymer of an azetidinium-containing vinylic monomer, (b) a hydrophilicity-enhancing agent which is non-ionic or positively charged at the pH of the aqueous solution, which pH is at least 9.0, and has at least one reactive functional group selected from the group consisting of primary amino group, secondary amino group, thiol group, and a combination thereof, and (c) one or more non-polymeric ionic compounds which are present in the aqueous solution in a total amount of 1 mM to 120 mM and are selected from the group consisting of sodium chloride, potassium chloride, salts of phosphoric acid, salts of boric acid, salts of citric acid, salts of carbonic acid, and combinations thereof; and heating the reactive mixture to reach a reaction temperature of from about 40°C to about 85°C and maintaining the temperature of the reactive mixture at the reaction temperature for a time period sufficient to obtain the water-soluble thermally-crosslinkable polymeric material in which the hydrophilicity-enhancing agent is covalently attached to the azetidinium-containing polymer through one or more covalent linkages each formed between one azetidinium group and one reactive functional group,