Core-sheath composite fiber and method for producing same

A core-sheath composite fiber comprising a core component comprising an easily alkaline elutable polyester with a main repeating unit constructed of ethylene terephthalate containing 2.0 to 5.5 mol % of an isophthalic acid component containing a metal sulfonate group relative to a total acid component and 3.0 to 6.0 mol % of an adipic acid component relative to the total acid component, and a sheath component comprising a polyamide, wherein the easily alkaline elutable polyester and the polyamide react in an ester-amide exchange reaction at an interface of the easily alkaline elutable polyester and the polyamide and a unit reaction rate of a terephthalic acid that caused the ester-amide exchange reaction is 0.0005 to 0.0025%·mm, wherein the unit reaction rate is calculated from Equation (1):

• A(%·mm)=T/S (1)
• where A is the unit reaction rate, T is the reaction rate (%) of the terephthalic acid that caused the ester-amide exchange reaction, and S is the surface area of the core of the fiber axis portion per 1 mm3 of the core-sheath type composite section fiber (mm2/mm3);
• and
• wherein the S is calculated from Equation (2):
• S(mm2/mm3)=X(mm)×Y(mm/mm3)×correction coefficient (2)
• where (a) Core portion's circumference length (mm):
• X,
• (b) Fiber length (mm) for unit volume (1 mm3):
• Y (mm/mm3),
• (c) Correction coefficient=fiber diameter (calculated value)/fiber diameter (actually measured value);
• Y(mm/mm3)=1±fiber sectional area(calculated value);
• Fiber sectional area(mm2)=[fiber diameter(calculated value)/2]2×π;
• Fiber diameter(calculated value)(mm)=11.28×√(single yarn fineness degree/specific gravity of core-sheath composite fiber)×10−3;
• and
• Specific gravity of core-sheath composite fiber(g/cm3)specific gravity of core polymer×ratio of core+specific gravity of sheath polymer×ratio of sheath.