###### Abstract  
In this article, we present a nonlocal Cahn-Hilliard (nCH) equation incorporating a space-dependent parameter to model microphase separation phenomena in diblock copolymers. The proposed model introduces a modified formulation that accounts for spatially varying average volume fractions and thus captures nonlocal interactions between distinct subdomains. Such spatial heterogeneity plays a critical role in determining the morphology of the resulting phase-separated structures. To efficiently solve the resulting partial differential equation, a Fourier spectral method is used in conjunction with a linearly stabilized splitting scheme. This numerical approach not only guarantees stability and efficiency but also enables accurate resolution of spatially complex patterns without excessive computational overhead. The spectral representation effectively handles the nonlocal terms, while the stabilization scheme allows for large time steps. Therefore, this method is suitable for long-time simulations of  
terms. They also conducted numerical experiments to validate the second-order method through convergence tests and long-time coarsening simulations. [PERSON] et al. (2017) presented a comprehensive convergence analysis based on error consistency and stability estimates for the nCH equation. [PERSON] et al. (2018) developed and investigated a second-order linear numerical scheme for the nCH equation with the Fourier spectral collocation method. [PERSON] et al. (2019) proposed two classes of exponential temporal differencing methods for the nCH equation, using Fourier collocation while rigorously proving their energy stability and mass conservation. In this article, we present computational simulations of the nCH equation with a space-dependent parameter using the Fourier spectral method, which is a powerful computational method used to solve partial differential equations (PDEs), particularly those with periodic boundary conditions. This method is widely used in a variety of fields, such as fluid dynamics ([PERSON] et al., 2018), phase field models ([PERSON] et al., 2018), and quantum mechanics ([PERSON] et al., 2018). Countless studies ([PERSON] et al., 2018; [PERSON] et al., 2019; [PERSON] et al., 2019; [PERSON] et al., 2019) have proven the feasibility of this method. In particular, we propose a modified equation of the nonlocal CH equation ([PERSON] et al., 2018), given as follows:  
\[\frac{\partial\phi(\mathbf{x},t)}{\partial t}=\Delta\Big{(}F^{\prime}(\phi( \mathbf{x},t))-\epsilon^{2}\Delta\phi(\mathbf{x},t))\Big{)}-\sigma\big{(} \phi(\mathbf{x},t)-\overline{\phi}\big{)},\quad\mathbf{x}\in\Omega,\;\;t>0, \tag{1}\]  
where \(F(\phi)=0.25(\phi^{2}-1)^{2}\) is a double-well potential ([PERSON] et al., 2018). The parameter \(\epsilon\) represents the interfacial transition width and characterizes the thickness of the diffuse interface separating distinct phases; and it plays a crucial role in phase-field models by controlling the sharpness of the interface: smaller values of \(\epsilon\) lead to sharper interfaces that more closely approximate a classical sharp interface, while larger values produce smoother transitions ([PERSON] et al., 2018); \(\sigma\) is a positive parameter, and \(\overline{\phi}=\int_{\Omega}\phi(\mathbf{x},0)d\mathbf{x}/|\Omega|\). If \(\sigma=0\), then Equation (1) becomes the classical CH equation ([PERSON] et al., 2018). The CH equation is a nonlinear, fourth-order partial differential equation that models phase separation processes in binary mixtures, such as alloys, polymers, or fluids. It describes how two components in a mixture spontaneously separate and evolve over time to minimize the system's free energy. A block copolymer refers to a polymer composed of two or more covalently bonded homopolymeric segments arranged in a linear chain. Specifically, a diblock copolymer comprises two chemically distinct monomer units linked sequentially along the polymer backbone.